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In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.
Implication introduction / elimination (modus ponens) Biconditional introduction / elimination; Conjunction introduction / elimination; Disjunction introduction / elimination; Disjunctive / hypothetical syllogism; Constructive / destructive dilemma; Absorption / modus tollens / modus ponendo tollens; Negation introduction; Rules of replacement
and the principle of idempotency of conjunction: P ∧ P ⇔ P {\displaystyle P\land P\Leftrightarrow P} Where " ⇔ {\displaystyle \Leftrightarrow } " is a metalogical symbol representing "can be replaced in a logical proof with".
In logic, mathematics and linguistics, and is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ∧ {\displaystyle \wedge } [ 1 ] or & {\displaystyle \&} or K {\displaystyle K} (prefix) or × {\displaystyle \times } or ⋅ {\displaystyle \cdot } [ 2 ] in ...
Conjunction introduction / elimination; ... i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a ...
If is a formula, so is . If and are formulae ... Conjunction elimination: Simplification (S), [17] ampersand elimination [22] [17] m &E [17] [22] The same as at line m.
A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to
Propositions for which double-negation elimination is possible are also called stable. Intuitionistic logic proves stability only for restricted types of propositions. A formula for which excluded middle holds can be proven stable using the disjunctive syllogism, which is discussed more thoroughly below. The converse does however not hold in ...